Positive entropy actions of countable groups factor onto Bernoulli shifts

Seward, Brandon

doi:10.1090/jams/931

Positive entropy actions of countable groups factor onto Bernoulli shifts
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by Brandon Seward

J. Amer. Math. Soc. 33 (2020), 57-101

DOI: https://doi.org/10.1090/jams/931

Published electronically: September 27, 2019

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Abstract:

We prove that if a free ergodic action of a countably infinite group has positive Rokhlin entropy (or, less generally, positive sofic entropy), then it factors onto all Bernoulli shifts of lesser or equal entropy. This extends to all countably infinite groups the well-known Sinai factor theorem from classical entropy theory.

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